The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  1  1  2  4  1  0  1  4  1  2  0  1  4  1  0  4  1  4  2  1  1  1  1  1  1  2  1  1  6  1  1  1  2  1  4  1  0  4  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  1  2  3  1  0  0  5  1  2  7  1  2  6  1  2  0  1  1  2  3  1  5  1  1  1  2  1  7  7  5  2  2  7  1  6  5  0  3  3  2  0  2  1  4  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  1  1  1  0  1  1  2  3  2  3  2  3  1  0  2  3  1  2  1  1  1  1  2  2  3  0  1  3  0  3  2  1  3  3  2  2  2  1  2  0  1  1  1  2  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  2  0  6  0  6  2  0  2  2  0  2  0  4  2  6  2  0  0  2  6  4  6  6  2  2  0  2  2  6  6  4  2  6  0  6  6  4  6  4  4  2  0  0  2  4  6  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  4  0  0  0  0  4  0  0  4  4  4  4  0  4  0  4  0  4  4  4  0  0  0  0  0  0  4  0  4  0  0  4  4  4  0  0  4  0  0  0  4  4  4  4  0  0  0  0  0  0  4  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  4  0  0  0  4  0  4  4  0  4  0  4  0  4  4  4  0  4  4  0  0  4  0  4  0  0  0  0  4  4  4  0  0  4  4  4  4  4  0  4  4  4  0  4  4  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  4  0  0  4  4  4  4  4  0  4  4  4  0  0  0  0  4  0  0  0  4  0  4  4  0  4  0  0  0  0  4  0  0  4  4  0  4  4  4  0  4  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  4  0  4  4  4  0  4  4  0  4  0  0  0  4  0  0  4  4  0  4  4  0  4  0  4  4  4  4  4  4  4  4  4  4  0  4  0  0  0  0  0  0  4  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  4  4  4  0  4  0  0  4  0  4  4  4  4  0  4  4  4  4  4  0  0  4  0  0  4  0  0  0  0  0  4  4  4  0  0  0  4  0  0  0  4  4  4  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

generates a code of length 79 over Z8 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+16x^40+6x^41+31x^42+38x^43+72x^44+70x^45+125x^46+222x^47+255x^48+362x^49+444x^50+560x^51+684x^52+758x^53+780x^54+746x^55+657x^56+664x^57+529x^58+396x^59+302x^60+168x^61+127x^62+80x^63+54x^64+18x^65+24x^66+32x^67+66x^68+72x^69+204x^70+334x^71+847x^72+1012x^73+2074x^74+2260x^75+4604x^76+3988x^77+6536x^78+5004x^79+6484x^80+4108x^81+4640x^82+2306x^83+2124x^84+964x^85+828x^86+294x^87+206x^88+92x^89+49x^90+22x^91+36x^92+22x^93+62x^94+86x^95+115x^96+230x^97+301x^98+352x^99+496x^100+552x^101+672x^102+816x^103+802x^104+770x^105+664x^106+584x^107+442x^108+388x^109+268x^110+176x^111+129x^112+82x^113+63x^114+26x^115+30x^116+10x^117+6x^118+2x^119+10x^120+5x^122

The gray image is a code over GF(2) with n=316, k=16 and d=80.
This code was found by Heurico 1.16 in 99.4 seconds.